MHT CET · Maths · Differential Equations
The differential equation of an ellipse whose major axis is twice its minor axis, is
- A \(x+4 y \frac{d y}{d x}=0\)
- B \(x-4 y \frac{d y}{d x}=0\)
- C \(x+2 y \frac{d y}{d x}=0\)
- D None of these
Answer & Solution
Correct Answer
(A) \(x+4 y \frac{d y}{d x}=0\)
Step-by-step Solution
Detailed explanation
For the given ellipse, we have \(\mathrm{a}=2 \mathrm{~b}\)
\(
\therefore \frac{\mathrm{x}^2}{4 \mathrm{~b}^2}+\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1 \Rightarrow \mathrm{x}^2+4 \mathrm{y}^2=4 \mathrm{~b}^2
\)
Differentiating both sides w.r.t., we get
\(
2 x+8 y \frac{d y}{d x}=0 \Rightarrow x+4 y \frac{d y}{d x}=0
\)
\(
\therefore \frac{\mathrm{x}^2}{4 \mathrm{~b}^2}+\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1 \Rightarrow \mathrm{x}^2+4 \mathrm{y}^2=4 \mathrm{~b}^2
\)
Differentiating both sides w.r.t., we get
\(
2 x+8 y \frac{d y}{d x}=0 \Rightarrow x+4 y \frac{d y}{d x}=0
\)
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